International Journal of Theoretical Physics

, Volume 33, Issue 4, pp 913–930 | Cite as

3-Manifolds for relativists

  • Domenico Giulini


In canonical quantum gravity certain topological properties of 3-manifolds are of interest. This article gives an account of those properties which have so far received sufficient attention, especially those concerning the diffeomorphism groups of 3-manifolds. We give a summary of these properties and list some old and new results concerning them. The appendix contains a discussion of the group of large diffeomorphisms of thel-handle 3-manifold.


Field Theory Elementary Particle Quantum Field Theory Quantum Gravity Topological Property 
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  1. Aneziris, C., Balachandran, A. P., Bourdeau, M., Jo, S., Ramadas, T. R., and Sorkin, R. (1989),International Journal of Modern Physics A,4, 5459–5510.Google Scholar
  2. Coxeter, H. S. M. and Moser, W. O. J. (1965).Generators and Relations for Discrete Groups, 2nd edition, Springer-Verlag, Berlin, Göttingen, Heidelberg, New York.Google Scholar
  3. Friedman, J., and Sorkin, R. (1980).Physical Review Letters,44, 1100–1103.Google Scholar
  4. Gibbons, G. W., and Hawking, S. W. (1992).Communications in Mathematical Physics,148, 345–352.Google Scholar
  5. Giulini, D. (1992a). On the configuration space topology in general relativity, Preprint, Freiburg THEP-92/32 and gr-qc 9301020, submitted for publication.Google Scholar
  6. Giulini, D. (1992b).Communications in Mathematical Physics 148, 353–357.Google Scholar
  7. Giulini, D. (1993). Quantum mechanics on spaces with finite non-Abelian fundamental group, in preparation.Google Scholar
  8. Giulini, D., and Louko, J. (1992).Physical Review D,46, 4355–4364.Google Scholar
  9. Gromov, M., and Lawson, B. (1983).Institut des Hautes Études Scientifique Publicationes Mathematiques,58, 294–408.Google Scholar
  10. Hartle, J., and Witt, D. (1988).Physical Review D,37, 2833–2836.Google Scholar
  11. Hempel, J. (1976).3-Manifolds, Princeton University Press, Princeton, New Jersey.Google Scholar
  12. Hendriks, H., and Laudenbach, F. (1984).Topology,23, 423–443.Google Scholar
  13. Hendriks, H., and McCullough, D. (1987).Topology and its Application,26, 25–31.Google Scholar
  14. Isham, C. J. (1981).Physics Utters B,106, 188–192.Google Scholar
  15. Laudenbach, F. (1974).Asterisque,12, 1–137.Google Scholar
  16. Lee, K. B., Shin, J., and Yokura, S. (1993). Free actions of finite Abelian groups on the 3-torus, University of Oklahoma preprint.Google Scholar
  17. McCullough, D. (1986).Geometric and Algebraic Topology (Warsaw),18, 61–76.Google Scholar
  18. Milnor, J. (1971).Introduction to Algebraic K-Theory. Princeton University Press, Princeton, New Jersey.Google Scholar
  19. Orlik, P. (1972).Seifert Manifolds, Springer-Verlag, Berlin.Google Scholar
  20. Rourke, C., and de Sá, C. (1979).Bulletin of the American Mathematical Society, (New Series)1, 251–254.Google Scholar
  21. Sorkin, R. (1989). Classical topology and quantum phases: Quantum geons, inGeometrical and Algebraic Aspects of Nonlinear Field Theory, S. De Filippo, M. Marinaro, G. Marmo, and G. Vilasi, eds., Elsevier, North-Holland.Google Scholar
  22. Thomas, C. B. (1986).Elliptic Structures on 3-Manifolds, Cambridge University Press, Cambridge.Google Scholar
  23. Thomas, C. B. (1988).Bulletin of the London Mathematical Society,20, 65–67.Google Scholar
  24. Witt, D. (1986).Journal of Mathematical Physics,27, 573–592.Google Scholar
  25. Witt, D. (1987). Topological obstructions to maximal slices, Santa Barbara preprint, UCSB-1987.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Domenico Giulini
    • 1
  1. 1.Fakultät für PhysikUniversität FreiburgFreiburg i.Br.Germany

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